Question: Simplify the following expression: $q = \dfrac{y^2 - 7y + 10}{y - 2} $
First factor the polynomial in the numerator. $ y^2 - 7y + 10 = (y - 2)(y - 5) $ So we can rewrite the expression as: $q = \dfrac{(y - 2)(y - 5)}{y - 2} $ We can divide the numerator and denominator by $(y - 2)$ on condition that $y \neq 2$ Therefore $q = y - 5; y \neq 2$